Mathematics
In the figure (i) given below, CDE is an equilateral triangle formed on a side CD of a square ABCD. Show that △ADE ≅ △BCE and hence, AEB is an isosceles triangle.
Triangles
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Answer
From figure,
∠ADE = ∠ADC + ∠CDE = 90° + 60° = 150°.
Similarly,
∠BCE = ∠BCD + ∠DCE = 90° + 60° = 150°.
⇒ ∠ADE = ∠BCE.
AD = BC (As sides of squares are equal)
DE = EC (As CDE is an equilateral triangle.)
∴ △ADE ≅ △BCE by SAS axiom.
We know that corresponding parts of congruent triangles are equal.
∴ AE = BE.
Hence, proved that AE = BE i.e. AEB is an isosceles triangle.
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